Problem: Simplify the following expression: $a = \dfrac{-3z^2 + 9z + 162}{z + 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ a =\dfrac{-3(z^2 - 3z - 54)}{z + 6} $ Then we factor the remaining polynomial: $z^2 {-3}z {-54} $ ${6} {-9} = {-3}$ ${6} \times {-9} = {-54}$ $ (z + {6}) (z {-9}) $ This gives us a factored expression: $\dfrac{-3(z + {6}) (z {-9})}{z + 6}$ We can divide the numerator and denominator by $(z - 6)$ on condition that $z \neq -6$ Therefore $a = -3(z - 9); z \neq -6$